Accessibility model:
N = Σi Σj Pi · Ej · τijθ
where
τij = shortest path with weight
K·d for roads, 1·d for bike lanes
Legend - Lanes
Existing lanes
Under construction
Wishing list
Selected lane
User-drawn lane
Path on bike lane
Path on road
Area Accessibility (log scale)
LowHigh
Select Wishing Lanes
Click lanes to select them for the network. Selected lanes affect path finding and accessibility calculations.
Draw Custom Lanes
Draw your own bike lanes on the map to test their impact on accessibility. Click points to create a lane path, double-click to finish.
Your Drawn Lanes (0)
Compute Accessibility
Calculate accessibility for current network with selected lanes. This computes all area-to-area distances (30-60 sec).
Selected lanes:0
Parameters: K=100, θ=-1.0, Year=2025
Find Shortest Path
Compute shortest path using current network (with selected lanes).
Not set - click Pick
Not set - click Pick
Rank Lanes
Calculate the contribution of each lane to network accessibility. Choose a ranking mode below.
Additive mode: Measures the value each lane would add if built next. Baseline is the currently selected lanes.
Parameters: K=100, θ=-1.0, Year=2025
Jerusalem Bike Lane Analysis - Methodology
Overview
This tool ranks proposed ("wishing list") bike lanes by their potential contribution to city-wide accessibility. It uses a gravity-based accessibility model to measure how well people can reach jobs across the city, with bike lanes significantly reducing the effective travel cost.
The Accessibility Model
Core Formula
N = Σi Σj Pi × Ej × τijθ
Where:
Pi = Population of area i (potential trip origins)
Ej = Employment in area j (potential trip destinations)
τij = Travel cost (shortest path distance in km) from area i to area j
θ = Distance decay parameter (negative, typically -1 to -2)
Parameters
K - No-Lane Penalty
Roads without bike lanes are penalized by multiplying their length by K:
weight = length for roads WITH bike lanes
weight = length × K for roads WITHOUT bike lanes
Higher K values mean cyclists strongly prefer bike lanes: K=10 (mild), K=100 (strong, default), K=500 (very strong).
θ (Theta) - Distance Decay
Controls how quickly accessibility decreases with distance:
θ = -0.5: Slow decay (long trips acceptable)
θ = -1.0: Moderate decay (default)
θ = -2.0: Fast decay (only nearby destinations matter)
References:
Donaldson, D., & Hornbeck, R. (2016). Railroads and American economic growth: A "market access" approach. The Quarterly Journal of Economics, 131(2), 799-858.
Tsivanidis, N. (2024). Evaluating the Impact of Urban Transit Infrastructure: Evidence from Bogotá's TransMilenio. American Economic Review, 116(2), 418-463.
Data Sources
Data
Source
Year
Statistical Areas
Jerusalem Transportation Master Plan Team
2025 projections
Population (pop_2025)
Jerusalem Transportation Master Plan Team
2025 projections
Employment (emp_2025)
Jerusalem Transportation Master Plan Team
2025 projections
Completed Bike Lanes
Jerusalem Transportation Master Plan Team
Current
Under Construction Bike Lanes
Jerusalem Transportation Master Plan Team
Current
Wishing List Bike Lanes
The author
Proposed
Road Network
OpenStreetMap
Current
Road Network Construction
The road network is built from Jerusalem road data (from OpenStreetMap, KML format) with the following process:
Node Creation: Road endpoints are snapped to a grid (15m tolerance) to create a connected graph
Edge Creation: Each road segment becomes an edge with its physical length as the base weight
Bike Lane Matching: Existing bike lanes are spatially matched to road edges using a 15m buffer and 50% overlap threshold
Coordinate Systems: Calculations use Israeli TM (EPSG:2039) for accurate distance; display uses WGS84 (EPSG:4326)
Network Connectivity
The tool ensures the network is fully connected through several mechanisms:
Node Merging
Tolerance: Nodes within 15 meters are merged into a single node
Purpose: Handles imprecise GPS coordinates and ensures lane endpoints connect properly to roads
Intersection Detection
Bike lanes are overlaid on the road network
Intersection points between bike lanes and roads are detected automatically
New nodes are created at every intersection point
Edges are split at intersection points to enable routing through the network
Gap Connection Algorithm
For bike lanes with gaps between segments:
Endpoint Extraction: Extract start and end points from all lane geometries
KD-Tree Indexing: Build spatial index for efficient nearest-neighbor queries
Dangling Endpoint Detection: Identify endpoints not touching other lanes (within 1m tolerance)
Gap Bridging: Connect dangling endpoints to nearest neighbor within 50m tolerance
Component Connection
For disconnected network components:
Component Detection: Find all connected components using graph algorithms
Minimum Spanning Tree Approach: Connect isolated components by adding edges between closest nodes
This connectivity fixing is essential because raw GIS data often has small gaps, coordinate mismatches, or isolated segments that would otherwise break shortest path calculations.
Shortest Path Algorithm
We use Dijkstra's algorithm to compute shortest paths between all area centroids:
Graph: Undirected weighted graph where edge weight = length × K for roads without bike lanes
Source: Nearest network node to each area centroid
Output: Distance matrix τij between all area pairs
Reference: Dijkstra, E.W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1), 269-271.
Online Computation
All accessibility calculations are performed in the browser using JavaScript:
Baseline Computation: When K or θ changes, compute accessibility with existing lanes only
Network Update: When wishing lanes are selected, mark their corresponding road edges as bike lanes (weight = length instead of length × K)
Full Recomputation: Run Dijkstra from each of the ~200 area centroids to compute new τij matrix
Accessibility Aggregation: Sum Pi × Ej × τijθ for all pairs
How Lanes Are Ranked
Baseline Calculation: Compute total N using existing bike lanes only
With Selected Lanes: Add selected wishing lanes and recompute N